I was going to say I would move her with everything in the same configuration as you currently have it then let her roam once she's settled...but it looks like you already got your answer. 😂🫣 Hope it goes ok moving forward!
A standard pet gate (taller than baby gates) reinforced with mesh would work, on the inside or outside of the door.
You might also want to look into a double door type system if taking up a bit of space isn't a concern... I used a temporary one whilst current bun settled in as I have a dog and...
Are you looking to leave it in place permanently? Argos do a pet gate with really small holes for around £20. It's pressure fit and pretty sturdy however it is only about 60cm tall (wouldn't be an issue if the main door is behind/in front, obviously) and not the best if you're using it...